//=====================================================================================================
// MadgwickAHRS.c
//=====================================================================================================
//
// Implementation of Madgwick's IMU and AHRS algorithms.
// See: http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms
//
// Date			Author          Notes
// 29/09/2011	SOH Madgwick    Initial release
// 02/10/2011	SOH Madgwick	Optimised for reduced CPU load
// 19/02/2012	SOH Madgwick	Magnetometer measurement is normalised
//
//=====================================================================================================

//---------------------------------------------------------------------------------------------------
// Header files

#include "MadgwickAHRS.h"

#include <math.h>

//---------------------------------------------------------------------------------------------------
// Definitions
#define RAD_TO_DEG 57.295779513082320876798154814105
#define sampleFreq 500.0f  // sample frequency in Hz
#define betaDef    10.0f   // 2 * proportional gain

//---------------------------------------------------------------------------------------------------
// Variable definitions

volatile float beta = betaDef;  // 2 * proportional gain (Kp)
volatile static float
    q0 = 1.0f,
    q1 = 0.0f, q2 = 0.0f,
    q3 = 0.0f;  // quaternion of sensor frame relative to auxiliary frame

//---------------------------------------------------------------------------------------------------
// Function declarations

static float invSqrt(float x);

//====================================================================================================
// Functions

void MadgwickAHRSetBeta(float beta_in) {
    beta = beta_in;
}

//---------------------------------------------------------------------------------------------------
// AHRS algorithm update

void MadgwickAHRSupdate(float gx, float gy, float gz, float ax, float ay,
                        float az, float mx, float my, float mz) {
    float recipNorm;
    float s0, s1, s2, s3;
    float qDot1, qDot2, qDot3, qDot4;
    float hx, hy;
    float _2q0mx, _2q0my, _2q0mz, _2q1mx, _2bx, _2bz, _4bx, _4bz, _2q0, _2q1,
        _2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3,
        q2q2, q2q3, q3q3;

    // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in
    // magnetometer normalisation) if((mx == 0.0f) && (my == 0.0f) && (mz ==
    // 0.0f)) { 	MadgwickAHRSupdateIMU(gx, gy, gz, ax, ay, az); 	return;
    // }

    // Rate of change of quaternion from gyroscope
    qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
    qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
    qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
    qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);

    // Compute feedback only if accelerometer measurement valid (avoids NaN in
    // accelerometer normalisation)
    if (!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
        // Normalise accelerometer measurement
        recipNorm = invSqrt(ax * ax + ay * ay + az * az);
        ax *= recipNorm;
        ay *= recipNorm;
        az *= recipNorm;

        // Normalise magnetometer measurement
        recipNorm = invSqrt(mx * mx + my * my + mz * mz);
        mx *= recipNorm;
        my *= recipNorm;
        mz *= recipNorm;

        // Auxiliary variables to avoid repeated arithmetic
        _2q0mx = 2.0f * q0 * mx;
        _2q0my = 2.0f * q0 * my;
        _2q0mz = 2.0f * q0 * mz;
        _2q1mx = 2.0f * q1 * mx;
        _2q0   = 2.0f * q0;
        _2q1   = 2.0f * q1;
        _2q2   = 2.0f * q2;
        _2q3   = 2.0f * q3;
        _2q0q2 = 2.0f * q0 * q2;
        _2q2q3 = 2.0f * q2 * q3;
        q0q0   = q0 * q0;
        q0q1   = q0 * q1;
        q0q2   = q0 * q2;
        q0q3   = q0 * q3;
        q1q1   = q1 * q1;
        q1q2   = q1 * q2;
        q1q3   = q1 * q3;
        q2q2   = q2 * q2;
        q2q3   = q2 * q3;
        q3q3   = q3 * q3;

        // Reference direction of Earth's magnetic field
        hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 +
             _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
        hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 +
             my * q2q2 + _2q2 * mz * q3 - my * q3q3;
        _2bx = sqrt(hx * hx + hy * hy);
        _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 -
               mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
        _4bx = 2.0f * _2bx;
        _4bz = 2.0f * _2bz;

        // Gradient decent algorithm corrective step
        s0 = -_2q2 * (2.0f * q1q3 - _2q0q2 - ax) +
             _2q1 * (2.0f * q0q1 + _2q2q3 - ay) -
             _2bz * q2 *
                 (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) +
             (-_2bx * q3 + _2bz * q1) *
                 (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) +
             _2bx * q2 *
                 (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
        s1 = _2q3 * (2.0f * q1q3 - _2q0q2 - ax) +
             _2q0 * (2.0f * q0q1 + _2q2q3 - ay) -
             4.0f * q1 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) +
             _2bz * q3 *
                 (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) +
             (_2bx * q2 + _2bz * q0) *
                 (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) +
             (_2bx * q3 - _4bz * q1) *
                 (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
        s2 = -_2q0 * (2.0f * q1q3 - _2q0q2 - ax) +
             _2q3 * (2.0f * q0q1 + _2q2q3 - ay) -
             4.0f * q2 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) +
             (-_4bx * q2 - _2bz * q0) *
                 (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) +
             (_2bx * q1 + _2bz * q3) *
                 (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) +
             (_2bx * q0 - _4bz * q2) *
                 (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
        s3 = _2q1 * (2.0f * q1q3 - _2q0q2 - ax) +
             _2q2 * (2.0f * q0q1 + _2q2q3 - ay) +
             (-_4bx * q3 + _2bz * q1) *
                 (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) +
             (-_2bx * q0 + _2bz * q2) *
                 (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) +
             _2bx * q1 *
                 (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
        recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 +
                            s3 * s3);  // normalise step magnitude
        s0 *= recipNorm;
        s1 *= recipNorm;
        s2 *= recipNorm;
        s3 *= recipNorm;

        // Apply feedback step
        qDot1 -= beta * s0;
        qDot2 -= beta * s1;
        qDot3 -= beta * s2;
        qDot4 -= beta * s3;
    }

    // Integrate rate of change of quaternion to yield quaternion
    q0 += qDot1 * (1.0f / sampleFreq);
    q1 += qDot2 * (1.0f / sampleFreq);
    q2 += qDot3 * (1.0f / sampleFreq);
    q3 += qDot4 * (1.0f / sampleFreq);

    // Normalise quaternion
    recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
    q0 *= recipNorm;
    q1 *= recipNorm;
    q2 *= recipNorm;
    q3 *= recipNorm;
}

//---------------------------------------------------------------------------------------------------
// IMU algorithm update

void MadgwickAHRSupdateIMU(float gx, float gy, float gz, float ax, float ay,
                           float az, float *pitch, float *roll, float *yaw) {
    float recipNorm;
    float s0, s1, s2, s3;
    float qDot1, qDot2, qDot3, qDot4;
    float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2, _8q1, _8q2, q0q0, q1q1,
        q2q2, q3q3;

    // Rate of change of quaternion from gyroscope
    qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
    qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
    qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
    qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);

    // Compute feedback only if accelerometer measurement valid (avoids NaN in
    // accelerometer normalisation)
    if (!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
        // Normalise accelerometer measurement
        recipNorm = invSqrt(ax * ax + ay * ay + az * az);
        ax *= recipNorm;
        ay *= recipNorm;
        az *= recipNorm;

        // Auxiliary variables to avoid repeated arithmetic
        _2q0 = 2.0f * q0;
        _2q1 = 2.0f * q1;
        _2q2 = 2.0f * q2;
        _2q3 = 2.0f * q3;
        _4q0 = 4.0f * q0;
        _4q1 = 4.0f * q1;
        _4q2 = 4.0f * q2;
        _8q1 = 8.0f * q1;
        _8q2 = 8.0f * q2;
        q0q0 = q0 * q0;
        q1q1 = q1 * q1;
        q2q2 = q2 * q2;
        q3q3 = q3 * q3;

        // Gradient decent algorithm corrective step
        s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
        s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 +
             _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
        s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 +
             _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
        s3        = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;
        recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 +
                            s3 * s3);  // normalise step magnitude
        s0 *= recipNorm;
        s1 *= recipNorm;
        s2 *= recipNorm;
        s3 *= recipNorm;

        // Apply feedback step
        qDot1 -= beta * s0;
        qDot2 -= beta * s1;
        qDot3 -= beta * s2;
        qDot4 -= beta * s3;
    }

    // Integrate rate of change of quaternion to yield quaternion
    q0 += qDot1 * (1.0f / sampleFreq);
    q1 += qDot2 * (1.0f / sampleFreq);
    q2 += qDot3 * (1.0f / sampleFreq);
    q3 += qDot4 * (1.0f / sampleFreq);

    // Normalise quaternion
    recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
    q0 *= recipNorm;
    q1 *= recipNorm;
    q2 *= recipNorm;
    q3 *= recipNorm;

    *pitch = asin(-2 * q1 * q3 + 2 * q0 * q2);  // pitch
    *roll  = atan2(2 * q2 * q3 + 2 * q0 * q1,
                  -2 * q1 * q1 - 2 * q2 * q2 + 1);  // roll
    *yaw   = atan2(2 * (q1 * q2 + q0 * q3),
                 q0 * q0 + q1 * q1 - q2 * q2 - q3 * q3);  // yaw

    *pitch *= RAD_TO_DEG;
    *yaw *= RAD_TO_DEG;
    // Declination of SparkFun Electronics (40°05'26.6"N 105°11'05.9"W) is
    // 	8° 30' E  ± 0° 21' (or 8.5°) on 2016-07-19
    // - http://www.ngdc.noaa.gov/geomag-web/#declination
    *yaw -= 8.5;
    *roll *= RAD_TO_DEG;
}

//---------------------------------------------------------------------------------------------------
// Fast inverse square-root
// See: http://en.wikipedia.org/wiki/Fast_inverse_square_root

static float invSqrt(float x) {
    float halfx = 0.5f * x;
    float y     = x;
    long i      = *(long *)&y;
    i           = 0x5f3759df - (i >> 1);
    y           = *(float *)&i;
    y           = y * (1.5f - (halfx * y * y));
    return y;
}

//====================================================================================================
// END OF CODE
//====================================================================================================
